Under the care of "optimistic" doctors, Jahi McMath -- whom a judge and other doctors have declared brain-dead, over her family's objections -- is "improving" days after her release from an Oakland, California, hospital, her family's lawyer said.

Attorney Chris Dolan detailed some of what's happened to the 13-year-old girl since her release Sunday from Children's Hospital & Research Center Oakland. After initially "doing poorly she is stabilizing," he said, adding that the teen underwent tracheotomy and gastrostomy tube procedures.

"She is doing very well and getting the treatment she should have gotten 28 days ago," Dolan said Wednesday, referring to what happened to Jahi after a December operation.

"Doctors are optimistic that her condition has stabilized and that her health is improving from when she was taken from (the Oakland hospital)."

The family hasn't said where the eighth-grader currently is. Dolan has declined to say if she had been transferred to another facility and, if so, to describe that facility.

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Instead, they have chosen to lie low as they continue their efforts to care for Jahi. Dolan said the family needs to "heal up from this whole experience" and have "some quiet time" away from media questions.

"(The) family is seeking to focus attention on Jahi," added the lawyer.

CNN could not independently verify Dolan's account about what's happened to the young California teen.

Jahi underwent a December 9 operation at the Northern California hospital to remove her tonsils, adenoids and extra sinus tissue.

Doctors had recommended the surgery to treat pediatric obstructive sleep apnea, a condition that made her stop breathing in her sleep and caused other medical problems.

The teen girl was alert and talking to doctors after the procedure, even asking for a Popsicle because her throat hurt. That was a relief in some ways because she'd expressed concerns to her family about the surgery, fearing she would never wake up from it, her uncle has said.

Due to privacy laws, hospital officials have not been able to discuss Jahi's case in detail.

In the hospital's intensive care unit, however, the girl started to bleed, her family has said, and she went into cardiac arrest. Days later, she was declared brain-dead. A judge later sided with the hospital in declaring her dead.

The family, however, did not agree.

That conflict played into a weeks-long battle between the hospital, which wanted to remove Jahi from a ventilator, and her family, who believed she was showing signs of life.

The entire ordeal fueled a sweeping national debate about what legally and ethically constitutes death.

Some medical ethicists have said the case has fed into a misperception that "brain death" is not death; that somehow, the body can live on, and that is life.

It's also sparked fierce emotion, and that is another reason the family is keeping quiet about where the girl will be taken.

"We've had people make threats from around the country," Dolan, who said he and the girl's uncle have received such threats, has told CNN. "It's sad that people act that way."